The Poker test for testing random number generators.
Usage
poker.test(u , nbcard = 5, echo = TRUE)
Arguments
u
sample of random numbers in ]0,1[.
echo
logical to plot detailed results, default TRUE
nbcard
a numeric for the number of cards,
we assume that the length of u is a multiple of nbcard.
Details
We consider a vector u, realisation of i.i.d. uniform random
variables U1... Un.
Let us note k the card number (i.e. nbcard).
The poker test computes a serie of 'hands' in {0, ..., k-1}
from the sample
u_i = floor(u_i k) (u must have a length dividable by k). Let
n_j be the number of 'hands' with (exactly) j different cards. The
probability is
p_j = 1/k^k * k! / (k-j)!) * S_k^j,
where S_k^j denotes the Stirling numbers of the second kind. Finally the
chi-squared statistic is
S = ∑_{j=1}^k [n_j - np_j/k ]^2/[np_j/k].
Value
a list with the following components :
statistic the value of the chi-squared statistic.
p.value the p-value of the test.
observed the observed counts.
expected the expected counts under the null hypothesis.
residuals the Pearson residuals, (observed - expected) / sqrt(expected).
Author(s)
Christophe Dutang.
References
Planchet F., Jacquemin J. (2003), L'utilisation de methodes de
simulation en assurance. Bulletin Francais d'Actuariat, vol. 6, 11, 3-69. (available online)
L'Ecuyer P. (2001), Software for uniform random number
generation distinguishing the good and the bad. Proceedings of the 2001
Winter Simulation Conference. (available online)
L'Ecuyer P. (2007), Test U01: a C library for empirical testing of
random number generators. ACM Trans. on Mathematical
Software 33(4), 22.
See Also
other tests of this package freq.test, serial.test, gap.test,
order.test and coll.test
ks.test for the Kolmogorov Smirnov test and acf for
the autocorrelation function.
Examples
# (1) hands of 5 'cards'
#
poker.test(runif(50000))
# (2) hands of 4 'cards'
#
poker.test(runif(40000), 4)
# (3) hands of 42 'cards'
#
poker.test(runif(420000), 42)